Role Contribution and Interpersonal Coordination in Partner-Assisted Flight According to Pair Experience

Abstract

Coordination refers to the relationship between elements. Likewise, in partner-assisted flight, gymnasts synchronize their movements to optimize performance. This work investigates the individual contribution of each gymnast for a paired task and the influence of pair experience on spatial-temporal variables and interpersonal coordination. Twelve national and international-level pairs performed ten vertical throws in laboratory settings. Data were collected using a motion capture system and processed using Theia Markerless software, v2023.1.0.3160.p14. Pairs were categorized by pair experience. Top gymnast motion was analyzed using global (GCS) and local coordinate systems (LCS), and spatial-temporal and cross-correlation variables were compared between experience levels. The results showed that the top gymnasts’ GCS exhibited the largest amplitudes, while the base and the top’s LCS demonstrated the smallest. More experienced pairs displayed a shorter downward motion (p < 0.001, Effect Size (ES) = 0.67) longer upward motion (p = 0.04, ES = 0.37), smaller time delays in position (p = 0.03, ES = 0.39), and longer time delays in velocity (p = 0.01, ES = 0.47). These findings suggest that top gymnasts’ motion is largely driven by the bases, and pair experience develops anticipation of the partner’s motion and task-specific adaptations. Increased partner training time appears crucial for improving interpersonal coordination.

1. Introduction

In traditional sports, such as figure skating, artistic swimming, cheerleading, or acrobatic gymnastics (ACRO), interpersonal coordination is crucial for the group’s acrobatic skills’ success [1]. Specifically, ACRO is a spectacular sport, where gymnasts perform balance and dynamic elements in pairs/groups [2]. Balance skills consist of pair/group static pyramids, and dynamic elements are characterized by maximum flight phases through partner-assisted flight [3]. In these exercises, the base gymnast throws and subsequently catches the top gymnast, effectively assisting the top gymnast’s flight. These elements are judged by the artistic merit, the difficulty, and above all by the execution, concerning the amplitude and technical correctness [3]. Judges consider the body stretch and tension, and fullness of movement, i.e., how much of the maximum space possible is used [3]. Despite the significance of these elements for performance, biomechanical studies on the subject remain scarce [4,5]. These literature reviews show that while research has evaluated the individual abilities of gymnasts practicing acrobatic gymnasts, only three studies evaluated static pyramids, and one congress article investigated a dynamic element, analyzing two pairs and exclusively assessing the motion of the top gymnast. This underlines a clear gap in the literature about both gymnasts’ movements and their impact on performance outcomes.

In biomechanics, coordination refers to the relation between elements working together to meet functional demands [6]. Interpersonal coordination, specifically, describes how the behavior of two or more individuals is brought into alignment [7]. This topic has been explored in synchronized trampoline [8] and crew rowing [9] from pedagogic and psychological perspectives, respectively. A biomechanical approach has been applied to crew rowing [10,11,12], four-legged coordination [13], horse riding [14,15], and during collective load carriage [16]. In ACRO, achieving amplitude during the flight phase [3] requires precise coordination between top and base gymnasts [17]. While top gymnasts jump with a motion similar to the countermovement jump (CMJ), base gymnasts throw, with a push press motion, combining a loaded lower-body countermovement with overhead pressing [18]. CMJ is extensively described using force-time curves [19,20,21,22,23], and the push press using vertical force and velocity-time curves [24]. In partner-assisted flight, the top gymnasts represent the load that the base gymnasts throw, although they are not a rigid body and may also contribute to the jump height, possibly through active push-off, body positioning, or timing adjustments. Thus, investigating this process of interpersonal coordination during partner-assisted flights could offer valuable insights into ACRO training.

To progress in ACRO, gymnasts rely on precise temporal coordination, and experienced gymnasts apply biomechanical knowledge to refine their technique and optimize performance [25]. In Artistic Gymnastics, experts exhibited larger vertical velocities and shorter contact times, suggesting that proper take-off conditions are major success predictors for vault, tumbling, and uneven bars [26,27,28]. Speed of movement was shown to increase at the intermediate-expert level [29]. Indeed, Hiley et al. [30] reported that as learning progresses, the technique and coordination seem to reach elite performer status. In group tasks, the horse–rider interaction differed between levels for waveform parameters, phase shifts, and riders’ posture [31]. This interaction was defined as the time lag between the rider and the horse: the smaller the lag, the better the coordination [14]. In ACRO, a congress investigation showed that the pair’s experience influences interpersonal coordination, with higher experience showing greater serial coordination modes [32]. Thus, difficulties in coordinating the pre-flight actions should affect the flight amplitude, and less experienced pairs should present more difficulties in coordinating these actions by using longer time delays and less similarity in their motion.

There is also uncertainty among ACRO coaches regarding the contribution of the top and base gymnasts during partner-assisted flights, with the assumption that a greater part of the work is performed by the base gymnast. In kinematic analyses, motion is generally estimated in relation to the laboratory’s global coordinate system (GCS). However, in the context of interpersonal coordination, the top gymnast’s movement is influenced by the base’s motion (i.e., top gymnast motion = top gymnast motion + base gymnast motion). Alternatively, the tops’ motion can be calculated independently of the bases by using a local coordinate system (LCS), defined as the mid-point between the base’s hands. In this approach, the LCS moves with the base gymnast’s hands [33], functioning like a moving floor against which the top gymnast generates a jump impulse. This method enables a clearer distinction between the independent contributions of the top gymnast and the influence of the base’s movement. To the best of our knowledge, no studies have been conducted on the individual contribution of the top gymnast to the overall system behavior.

This work aims to investigate: (1) the individual contribution of each gymnast to the motion of the system (using a GCS or LCS for the top gymnast); (2) the influence of the pair experience on spatial-temporal variables; and (3) on interpersonal coordination. We hypothesized the following: (1) LCS reveals the different contributions of each gymnast; (2) there are differences in spatial-temporal variables between experience levels, with a higher experience translates into faster movements; and (3) the interpersonal coordination differs between experience levels, with higher experience being associated with smaller time delays [14].

2. Materials and Methods

2.1. Sample Characterization

This investigation included base and top gymnasts from first division and elite level, competing at national and international level, with a minimal weekly training volume of 30 h. Twenty-one gymnasts (12 bases and 9 top gymnasts) volunteered to participate in this investigation.

The 12 base gymnasts included 8 females (age: 18.00 (3.12) (median interquartile range)) years, height: 1.64 (0.05) m, mass: 64.75 (7.56) kg and training experience: 8.00 (5.00) years) and 4 males (age: 16.50 (1.29) years, height: 1.71 (0.03) m, mass: 65.40 (6.07) kg and training experience: 5.00 (4.00) years). The 9 top gymnasts included 7 females (age: 13.14 (2.80) years, height: 1.45 (0.04) m, mass: 34.56 (3.73) kg and training experience: 6.00 (1.00) years) and 2 males (age: 13.00 (1.41) years, height: 1.43 (0.17) m, mass: 39.80 (9.48) kg and training experience: 9.50 (5.00) years).

Participants were grouped in 12 pairs of ACRO (8 female pairs, 1 mixed pair, and 3 male pairs), where 3 top gymnasts were grouped with 2 different bases to increase the number of pairs. The 12 pairs were further divided into two groups, using the median of the experience of training together as a pair (3 months) as the grouping criteria. Accordingly, 7 pairs were classified as less experienced (LE), with a maximum of 3 months of training together, and 5 pairs were included in the more experienced (ME) group, corresponding to a minimum of one year of training together. Detailed information about the groups is provided in

Table 1. Characterization of the less experienced (LE) and more experienced (ME) groups.

	LE (N = 7)		ME (N = 5)
Variables	Base	Top	Base	Top
Age (years)	18.00 (7.00)	14.00 (5.00)	16.00 (0.00)	12.00 (1.00)
Mass (kg)	70.10 (15.60)	36.40 (9.20)	61.10 (5.40)	32.80 (0.10)
Height (m)	1.68 (0.07)	1.49 (0.10)	1.64 (0.09)	1.45 (0.05)
Experience as a pair (years)	0.25 (0.17)		2.00 (1.75)

Note: Values reported as median (interquartile range).

.

All participants, or their legal guardians, after being informed of the study’s purpose, procedures, benefits, and risks, gave their voluntary and informed consent to participate, in accordance with the Declaration of Helsinki and the research Ethics Committee of the Faculty of Sport of the University of Porto (CEFADE 02.2022, approved on 18 January 2022).

Gymnasts completed their usual warm-up and were given a free performance volume of ~15 min to adapt to the laboratory environment. Each pair performed 10 vertical throws, with 2–3 min of rest between each attempt. Data collection was performed using a set of 8 Miqus video cameras (Qualisys AB, Gothenburg, Sweden) operating at 85 frames per second, which allowed for the use of the higher resolution option (1920 × 1080 pixel). The capture volume encompassed the pair, as well as the top’s flight path, and was calibrated using a wand. The maximum acceptable error for calibration was established as 0.80 mm. A 2 × 3 m gymnastics mat was placed adjacent to the base’s standing position as a safety measure against falls.

The gymnasts’ movement was processed using Markerless analysis software, v2023.1.0.3160.p14 (Theia Markerless, Inc., Kingston, ON, Canada) and the resulting 6 degrees of freedom models were exported to Visual3D, v2023.06.3 (C-Motion, Inc., Germantown, MD, USA) for further analysis. This included the calculation of the position and velocity of the center of mass (CoM) of the base and top gymnasts in relation to the laboratory’s global coordinate system (GCS). We also underline that this work focuses on the vertical axis (z), as the assessed skill occurs essentially in this axis.

2.2. Data Analysis Procedures

The top gymnast’s motion was also calculated in relation to a LCS, defined as the mid-point between the base’s hands. As such, the top LCS CoM position was calculated as the difference between the Top GCS CoM and the LCS position. The interaction between gymnasts was also analyzed as a system:

$${\mathrm{CoM}}_{\mathrm{sys}}={\displaystyle \frac{{\mathrm{CoM}}_{\mathrm{T}}\times {\mathrm{Mass}}_{\mathrm{T}}-{\mathrm{CoM}}_{\mathrm{B}}\times {\mathrm{Mass}}_{\mathrm{B}}}{{\mathrm{Mass}}_{\mathrm{T}}+{\mathrm{Mass}}_{\mathrm{B}}}},$$

(1)

the system’s CoM (CoM_sys) was calculated using the CoM (GCS) of each gymnast (top: CoM_T; base: CoM_B), and their contribution to the overall system mass (top: Mass_T; base: Mass_B). The system’s CoM velocity was calculated as the position’s first derivative.

Each trial began with the base gymnast standing while supporting the top gymnast, who was balanced on the base’s hands and stabilized on their shoulders. The movement onset was detected as the first instant when the top gymnast’s CoM presented a downward velocity. The take-off was detected through visual inspection of the last contact point between the base’s hands and the top’s feet. Two independent observers identified the take-off frame, and any discrepancies were discussed until a consensus was reached. For the characterization of each gymnast and the system’s motion, two phases were established according to the directionality of the CoM velocity.

For each curve analyzed, phase I started at the movement onset and finished at the CoM maximal downward position (MD Pos). This phase included the CoM maximum downward velocity (MD Vel) and continued until reaching zero velocity, which corresponded to the MD Pos [19,23]. For the base gymnast, this motion is similar to the unweighting and eccentric braking of the push press [24]. Phase II began at the instant of zero velocity, at which Phase I ended, and finished at take-off. During this period, the CoM velocity increases in an upward direction [19], featuring the maximum CoM upward velocity (MU Vel) [23]. In the push press, this is defined as concentric propulsion [24].

After take-off, the top gymnast is in free flight, with gravity being the only force acting upon them [23], and the base’s CoM movement becomes unrelated to the top’s flight trajectory. Thus, the top’s flight and the base’s motion after take-off are not in the scope of this study.

Four CoM position and velocity–time curves were analyzed for each trial: (1) the base gymnast; (2) the top gymnast; (3) the top gymnast from the LCS; and (4) the system. The following variables were extracted to characterize the movement: (i) the trial duration; (ii) each phase duration; (iii) the MD Pos and MD Vel; (iv) MU Vel; and (v) CoM position and velocity at take-off (TO Pos and TO Vel). A custom MATLAB, version R2023b (MathWorks, Natick, MA, USA) routine was used for the extraction of these variables. The initial position and velocity of each time curve was set to zero at the starting position, and the trial duration normalized. The position and velocity were analyzed as absolute values and normalized to the gymnasts’ stature. For the system, the sum of the top and base gymnasts’ height was considered.

To study the interpersonal coordination, the time-normalized curves of the CoM position and velocity were analyzed using cross-correlation between the entire signals. This procedure was performed in MATLAB, allowing to quantify the similarity between the base and top gymnasts’ curves (GCS and LCS) of different experience levels. The higher the cross-correlation between two signals at a given time lag, the higher their similarity [34]. The variables used for analysis were the zero-lag correlation index (r₀), the maximal correlation index (r_max), and its time lag [35]. The r₀ represents the correlation index at the zero-time lag [36], the r_max refers to the highest similarity between signals, and the time lag refers to the temporal delay of one signal relative to the other [37]. Coefficients vary between −1 and +1: a positive correlation indicates the time-varying signals are increasing and decreasing together, reflecting similar movements or alignment between both gymnasts’ actions, and a negative correlation indicates an inverse relationship, with distinct or opposing movements between gymnasts [37].

2.3. Statistical Analysis

Statistical analysis was performed using IBM SPSS Statistics for Windows, Version 27.0. Armonk, NY, United States. The non-normal distribution of the data were confirmed through a Shapiro–Wilk’s test. Data are presented as median (interquartile range). Two databases were used for this investigation: one for characterizing the curves in spatial-temporal features and a second one for cross-correlation analysis.

The Mann–Whitney tests were performed to compare the following: (1) the use of the GCS or the LCS for the top gymnast; (2) spatial-temporal variables between levels of experience from the curves from the base, top GCS, top LCS, and the system; and (3) the cross-correlation results between LE and ME pairs. Descriptive analysis was obtained for all variables. A significance level was set at p ≤ 0.05. Cohen’s d effect size was estimated [38,39], and the general guidelines for interpretation were as follows: 0.1 as small, 0.3 as moderate, and ≥0.5 as large relationships [40].

3. Results

The results showed different patterns in the CoM position and velocity of the base and top gymnasts, either individually, but also when considered as a system. Figure 1 depicts the gymnasts’ movements, and how those translate in terms of their individual CoM position and velocity. This figure demonstrates one execution of one pair participating in the study.

It is possible to identify different amplitudes in each curve. Top GCS display the largest amplitude, and the base and top LCS are the smallest. The system curve remains in the middle position between the base and the top gymnast (GCS). Position and velocity from the top LCS are smaller in magnitude, compared to the top GCS (p < 0.001).

Table 2. Comparison between spatial-temporal variables of less experienced (LE) and more experienced (ME) bases, tops using the global coordinate system (GCS), tops using the local coordinate system (LCS), and systems.

Variables	Unit	BASE			TOP GCS			TOP LCS			SYSTEM
		LE	ME	p (ES)	LE	ME	p (ES)	LE	ME	p (ES)	LE	ME	p (ES)
Trial Duration	s	1.72 (1.47)	1.58 (0.14)	<0.001 (0.80)	1.72 (0.47)	1.58 (0.14)	<0.001 (0.80)	1.72 (0.47)	1.58 (0.14)	<0.001 (0.80)	1.72 (0.47)	1.58 (0.14)	<0.001 (0.80)
Phase I	s	1.11 (0.42)	0.95 (0.24)	<0.001 (0.61)	1.13 (0.41)	0.99 (0.20)	<0.001 (0.72)	1.18 (0.37)	1.03 (0.11)	<0.001 (0.82)	1.12 (0.41)	0.98 (0.22)	<0.001 (0.67)
	%time	63.09 (7.89)	59.44 (11.66)	0.02 (0.43)	65.18 (7.49)	61.99 (6.19)	<0.001 (0.68)	66.68 (6.24)	64.49 (4.17)	<0.001 (0.77)	64.14 (8.49)	60.79 (7.82)	<0.001 (0.62)
Phase II	s	0.61 (0.06)	0.56 (0.11)	<0.001 (0.60)	0.58 (0.06)	0.58 (0.07)	0.37 (0.16)	0.56 (0.10)	0.56 (0.09)	0.45 (0.14)	0.58 (0.05)	0.56 (0.09)	0.04 (0.37)
	%time	36.91 (7.89)	40.56 (11.66)	0.02 (0.43)	34.82 (7.49)	38.01 (6.19)	<0.001 (0.68)	33.32 (6.24)	35.51 (4.17)	<0.001 (0.77)	35.86 (8.49)	39.21 (7.82)	<0.001 (0.62)
MD Pos	m	−0.24 (0.03)	−0.25 (0.03)	0.89 (0.03)	−0.61 (0.08)	−0.63 (0.06)	0.02 (0.43)	−0.27 (0.06)	−0.29 (0.03)	0.13 (0.27)	−0.37 (0.03)	−0.39 (0.03)	0.07 (0.33)
	stature	−0.14 (0.02)	−0.15 (0.02)	0.30 (0.19)	−0.42 (0.03)	−0.46 (0.03)	<0.001 (0.67)	−0.19 (0.04)	−0.20 (0.02)	0.02 (0.41)	−0.12 (0.01)	−0.13 (0.01)	0.005 (0.53)
TO Pos	m	0.09 (0.04)	0.09 (0.02)	0.06 (0.35)	0.67 (0.05)	0.63 (0.07)	<0.001 (0.75)	0.08 (0.04)	0.09 (0.04)	0.05 (0.36)	0.30 (0.05)	0.27 (0.05)	<0.001 (0.77)
	stature	0.06 (0.02)	0.05 (0.02)	0.17 (0.25)	0.45 (0.06)	0.45 (0.05)	0.11 (0.29)	0.06 (0.03)	0.07 (0.03)	0.02 (0.43)	0.10 (0.01)	0.09 (0.02)	0.009 (0.50)
MD Vel	m/s	−0.44 (0.15)	−0.48 (0.18)	0.06 (0.35)	−1.12 (0.38)	−1.21 (0.29)	<0.001 (0.64)	−0.56 (0.28)	−0.62 (0.15)	0.005 (0.53)	−0.66 (0.23)	−0.72 (0.22)	0.007 (0.51)
	stature/s	−0.44 (0.15)	−0.48 (0.18)	0.01 (0.45)	−0.75 (0.21)	−0.88 (0.23)	<0.001 (0.75)	−0.36 (0.19)	−0.44 (0.09)	<0.001 (0.63)	−0.21 (0.07)	−0.23 (0.08)	<0.001 (0.64)
MU Vel	m/s	1.39 (0.18)	1.45 (0.15)	0.02 (0.41)	3.59 (0.32)	3.47 (0.31)	0.02 (0.43)	1.60 (0.27)	1.37 (0.23)	<0.001 (0.90)	2.13 (0.23)	2.18 (0.24)	0.68 (0.08)
	stature/s	1.39 (0.18)	1.45 (0.15)	<0.001 (0.61)	2.47 (0.24)	2.48 (0.18)	0.68 (0.07)	1.08 (0.13)	0.98 (0.14)	<0.001 (0.73)	0.69 (0.05)	0.72 (0.10)	<0.001 (0.31)
TO Vel	m/s	−0.55 (0.16)	−0.55 (0.14)	0.84 (0.04)	2.45 (0.39)	2.54 (0.51)	0.48 (0.13)	2.03 (0.54)	2.04 (0.95)	0.45 (0.14)	0.51 (0.17)	0.53 (0.22)	0.97 (0.01)
	stature/s	−0.33 (0.10)	−0.34 (0.11)	0.34 (0.17)	1.68 (0.29)	1.81 (0.31)	0.07 (0.33)	1.39 (0.43)	1.42 (0.57)	0.81 (0.04)	0.16 (0.05)	0.18 (0.08)	0.59 (0.01)

Legend: Values reported as median (interquartile range). MD, maximum downward; Pos, position; TO, take-off; Vel, velocity; MU, maximum upward. Statistically significant differences are highlighted in bold. p ≤ 0.05, ES, effect-size [40].

depicts the results from the comparison between the spatial-temporal variables of LE and ME bases, tops GCS, tops LCS, and systems.

Compared to LE, ME pairs take less time to perform the same task. ME gymnasts are faster during Phase I, and ME bases and systems are faster in Phase II. When relative time is considered, ME gymnasts spend more time in Phase II, compared to LE.

ME tops GCS, LCS and systems achieved a lower MD Pos. ME tops LCS present a higher TO Pos, and ME tops GCS and systems achieved a lower TO Pos. In the MD Vel, ME gymnasts were faster. In MU Vel, ME bases and systems were faster, and ME tops GCS and LCS were slower. TO Vel was similar between experience levels.

Table 3. Cross-correlation results between the curves from the top global coordinate system (GCS) and base, and between the base and top local coordinate system (LCS) of less experienced (LE) and more experienced (ME) pairs. Indexes of cross-correlation (r) are presented for the maximal cross-correlation (r_max) and for lag = 0 (r₀) of position and velocity.

Variables	TOP GCS-BASE			TOP LCS-BASE
	LE	ME	p (ES)	LE	ME	p (ES)
Position rmax	0.98 (0.01)	0.98 (0.01)	0.45 (0.14)	0.97 (0.02)	0.98 (0.01)	0.02 (0.43)
Position r0	0.98 (0.02)	0.98 (0.01)	0.81 (0.04)	0.95 (0.04)	0.96 (0.02)	<0.001 (0.64)
Position lag (%movement)	0.90 (1.00)	0.65 (1.00)	0.03 (0.39)	2.80 (2.60)	1.40 (4.00)	<0.001 (0.62)
Velocity rmax	0.95 (0.03)	0.96 (0.02)	0.20 (0.24)	0.84 (0.10)	0.85 (0.05)	0.28 (0.20)
Velocity r0	0.82 (0.10)	0.82 (0.06)	0.36 (0.17)	0.78 (0.16)	0.82 (0.07)	0.01 (0.48)
Velocity lag (% movement)	5.10 (2.20)	5.75 (1.00)	0.01 (0.47)	−1.20 (4.50)	−1.75 (3.80)	0.06 (0.34)

Legend: Values reported as median (interquartile range). Lag: the time delay between r_max and r₀. Statistically significant differences are highlighted in bold. p ≤ 0.05, ES, effect-size [40].

depicts the results from the cross-correlation analysis of position and velocity curves.

Table 3 shows the top GCS-base analysis, where the ME pairs display shorter position lags and longer velocity lags, compared with the LE pairs. For the top LCS-base analysis, there are differences in all the position variables and in the velocity r₀, indicating higher correlations for the ME group. The velocity lag is similar between experience levels.

For the lag interpretation, the position results show that the top GCS and LCS are moving ahead of the base in both groups. The velocity lag depicts that the top GCS is also moving ahead of the base in both levels, and the top LCS is delayed in relation to the base.

4. Discussion

This study investigated the CoM position and velocity of the top gymnast, the base gymnast, and the overall system. The application of the LCS revealed distinct patterns in the position and velocity curves, highlighting the distinct contributions of each role, particularly the top gymnast’s. Differences were found between the spatial-temporal variables according to the experience level of the pairs, with higher experience translating into faster movements, potentially reflecting more efficient coordination and control. Cross-correlation results indicated that ME pairs exhibit smaller time delays in position curves, suggesting better synchronization, while the longer time delays observed in velocity curves may reflect more refined adaptations to task demands. These findings contribute to a better understanding of how experience influences interpersonal coordination in ACRO biomechanics, offering insights into training practices that may enhance performance and safety.

Since no studies were found describing the kinematics of acrobatic gymnasts performing partner-assisted flight, our first approach was to describe the movement, as the first step for understanding and analyzing motion [41]. Our results showed different amplitudes for each position and velocity curve, underlining different participations for each role. Since bases present larger anthropometric measurements [42] and are responsible for throwing the top, there is an assumption that the movement of the bases is the major contributor to the pair’s motion. Accordingly, the motion of the top GCS is dependent on the base’s position, while the top LCS occurs only due to the individual motion of this gymnast. For example, in Figure 1, the TO Pos of the top LCS results from the top gymnast’s own body extension and the raising of the upper limbs, while the TO Pos of the top GCS also incorporates the movement of the base gymnast. The reduced independent movement observed in the top gymnast, particularly in the LCS, indicates a more passive role during skill execution. This passivity may stem from factors such as fear of falling or uncertainty about controlling the aerial phase. Such behaviors can impact the gymnast’s ability to actively contribute to the movement, potentially affecting overall performance. Recognizing these patterns can help coaches implement specific drills to build confidence, encourage more active participation, and improve coordination with the base gymnast.

We also highlight that between MU Vel and TO Vel, the top LCS curve shows a relevant downward motion, followed by an upward motion just before take-off (Figure 1), which may represent a preparatory mechanism for coping with the aerial phase. In parallel, King and Yeadon [43] reported that proper timing during take-off allowed to cope with moderate perturbations of the approach characteristics, and that elite performance also requires in-flight adjustments [44]. For assessing the individual contribution of each gymnast, the use of the GCS reveals the movement performed by the base but does not reveal the movement that the top performs on its own, without the influence of the base. The top LCS measurement provides coaches and researchers with insightful information about this gymnast’s motion. Coaches must learn to observe the system, examining the base actions, but also understanding the top’s own ability to generate impulse or to allow the base gymnast to generate it. Similarly, in collective load carriage, one participant also made greater efforts than the other as a coordination strategy [16]. Thus, the use of the LCS confirmed that tops present limited independent movement and are primarily influenced by the base’s motion. Regarding the experience level, ME tops LCS present a higher TO Pos, which could suggest higher participation over experience, and ME tops GCS and LCS achieved lower MU Vel, indicating higher efficiency (only using the necessary velocity to conduct the aerial phase). Studies should focus on evaluating this tendency in distinct gymnastics skills.

When comparing spatial-temporal variables across experience levels, ME pairs were faster in the entire task and Phase I (downward movement), as expected, since higher training experience in gymnastics, shorter contact times, and faster movement are associated [25,26,27,28,45]. ME gymnasts performed Phase I faster, probably because they require less time to coordinate their downward actions, compared to LE. Possibly, they have also developed stronger eccentric braking. This mechanism demands a great volume of specific training to start to predict, control, and accommodate [46]. In Phase II, only ME bases and systems were faster, likely because ME bases are stronger and faster in the upward movement, and the major contributors to the system behavior, as seen previously. Studies have investigated the balance [47] and the jumping skills [16,48] of base and top gymnasts; however, the inclusion of different experience levels is recommended for a more accurate characterization.

When the entire trial is considered, different experience levels distribute the same amount of relative time differently. ME gymnasts spend significantly higher relative time in Phase II, when compared to LE, possibly because they are better coordinated, and may prioritize vertical displacement by actively extending the duration of upward motion. This could also be a strategy used to improve energy transfer from the top to the base gymnast, including the application of Hochmuth’s biomechanical principle of the temporal coordination of partial impulses [49]. In horse riding, riders also adapt temporally and spatially to the horse’s trunk movement to achieve and keep a well-adjusted seat [31]. Coaches and researchers should be aware that ACRO pairs spent more relative time in Phase I (around 60%) and less in Phase II (around 40%), regardless of the experience level, but a higher experience allows for a shorter downward movement and longer upward motion.

In spatial variables, a lower MD Pos was found for the ME tops GCS, LCS, and systems, but a higher TO Pos was found only for ME tops LCS. It is possible that ME tops can use a higher range of motion, but only ME tops LCS achieve higher TO Pos. Floría and Harrison [50] showed that females practicing ACRO increased their jump height by increasing the range of motion over which force is applied and that in adulthood, the focus should be to develop the skill to produce force throughout this range of motion. Nevertheless, these results seek validation for males. In MD Vel, all the ME gymnasts were faster. However, in MU Vel, ME bases and systems were faster, and ME tops GCS and LCS were slower, compared to LE. Research showed that a rigid or stable load is easier to balance [51], and the throw velocity decreases in unstable conditions [52]. Thus, ME bases and systems are faster possibly because ME tops are more stable (moving slower), since a stable load requires less time to press (reduced duration of concentric and eccentric phases) [53]. When lifting and moving a potentially unstable load, people tend to lift it more slowly compared with lifting a stable load [54]. In parallel, a better individual static balance in the headstand of the top gymnasts explained a better performance in the pyramids [55]. Possibly, ME tops are moving slower in this phase to allow for better force application by the base gymnast and/or the system, suggesting that ME tops are trying to move less while the bases are pushing them upward to improve skill performance.

While simulations in Artistic Gymnastics showed improved performances through increased CoM velocity and take-off height [56], our results show different MU Vel, but similar TO Vel between experience levels. In throwing activities, the maximal throwing velocity was used as a performance variable, i.e., in water polo [57] and in cricket, in which all sub-elite and elite groups displayed higher accuracy at velocities equivalent to 75–85% maximum [58]. Therefore, we underline that the lack of differences among experience groups in TO Vel may indicate that tops manage the velocities to perform the take-off fast enough to conduct the aerial trajectory, and not necessarily need to achieve the highest TO Vel possible. Also, the period between MU Vel and TO Vel of the top LCS, with a relevant downward and upward motion, could be an interesting alternative to check the effect of experience in future papers.

In interpersonal coordination analysis, the shorter position lag found for the ME group was expected, considering that elite athletes have a remarkable ability to anticipate future events through information sources from an opponent’s kinematics [59]. In ACRO, this anticipatory ability may result from consistent practice with a partner, where gymnasts learn to identify subtle cues from their partner’s posture, trajectory, and movement patterns. The inclusion of the top LCS-base analysis showed that curves from the ME gymnasts have a higher correlation, suggesting better coordination, likely because the ME gymnast can use biomechanical knowledge and adjust their technique for a more effective execution [25], i.e., adjust movement proactively, rather than reactively. In horse riding, an experienced rider controls their weight distribution and body movements during predictable gait-related events and responds quickly during unpredictable reactions of the horse (predictive and reactive strategies) [60]. Similarly, ME gymnasts appear to use biomechanical information to adjust their coordination more effectively, optimizing the timing and magnitude of their actions. Coaches can facilitate this development by incorporating variability in training tasks, encouraging gymnasts to adapt to changing movement patterns, and, consequently, improve their anticipation skills. Young performers can learn to anticipate, but only if the environment demands this behavior [59].

The results also showed that the top is moving ahead of the base, regardless of the experience. This is similar to the collective load carriage, where one subject may guide the movement while the other may follow it [16]. In ACRO, it is usual for the bases to wait for the tops to start to move and then follow their lead and adapt to their motion. A similar phenomenon occurs in trampoline. After reaching the MD Pos, the jumper typically adopts a near straight posture and propels themselves upward directly, receiving the restoring force from the trampoline bed, and returning to its original position [61]. The vertical deflection length of the trampoline bed and the upward velocity were determined by the downward phase [62]. According to our results, this technique could be applied in ACRO to optimize the interpersonal coordination, and coaches could give feedback for the tops to push down on the base hands (during the downward motion) and, after reaching the MD Pos, to straighten their body and wait for the base’s impulse. Bases would assume the role of the trampoline bed; therefore, they must wait for the stretching of the body of the top, and then to push. The analogy between ACRO and trampoline mechanics is supported by biomechanical similarities in force application and timing. In trampoline, the jumper’s downward motion stores energy in the bed, which is then released as upward kinetic energy. Similarly, in ACRO, the top’s downward motion provides a mechanical cue for the base to apply the upward impulse.

Longer time delays were found in velocity curves of ME pairs, compared to the LE. This may reflect an interpersonal coordination strategy for gymnasts to time their actions to achieve the maximum push. From a kinematic perspective, LE gymnasts might complete the movement quickly due to reduced familiarity with the timing requirements or a less efficient distribution of their time. This behavior could stem from a lack of confidence in the interaction forces or the anticipation of the next phase, leading to earlier or more abrupt transitions. Additionally, LE gymnasts may exhibit a more inconsistent trajectory of the CoM, without the refined temporal precision seen in ME pairs. LE gymnasts do not understand technique as easily as ME gymnasts due to limited training and skill development, and higher experience is related to smoother and faster preparation and take-off phase, as well as greater movement control [25]. Regardless of the experience level, when the base gymnast contribution is isolated (top LCS), the top is behind the base, indicating that the LCS reveals the individual contribution of the top not only in position but also in velocity curves. These distinct behaviors may alter the joint torques used and change the momentum at take-off [43]. In this work, both groups present time delays, regardless of the experience and the coordinate system. Simulations showed that errors in perceiving approach characteristics below 5% or 5º and timing activations below 7 m/s allow can be accommodated using adjustments during take-off and flight [43]. Further research is necessary to understand the impact of the time delay to perform different ACRO partner-assisted flight skills.

Finally, we would like to highlight the usefulness of normalizing the results to the subjects’ height. Although it is unusual in gymnastics, it was a strategy to remove the height bias between base and top gymnasts [42]. Using height normalization highlighted the small absolute velocity differences. In terms of limitations, we focused exclusively on the vertical axis (z), as the assessed skill occurs essentially in this axis. While a three-dimensional analysis could offer additional insights into interpersonal coordination, we chose to concentrate on the vertical component to allow for a more detailed and in-depth analysis. It would be interesting to investigate these processes in other gymnastic skills, perhaps including rotations of the top in the aerial phase. We also highlight that our approach was based on the analysis of the CoM, which is a simplification of the entire body to a single particle, therefore reflecting but not putting into evidence the complexity and interplay of each body segment movement. Finally, the sample size reflects the maximum number of pairs available within this performance level. To address this limitation, each pair completed 10 trials of the task, increasing the robustness of our findings. We acknowledge the challenges associated with recruiting gymnasts for laboratory-based research. We emphasize that these findings are specifically applicable to the experience levels assessed in this study (first division and elite levels) and may not extend to individuals with different training backgrounds or performance levels.

This work contributes to understanding how experience influences interpersonal coordination, providing insights that can guide new investigations in paired tasks. Empirically, these findings can be applied in practice by coaches and athletes to improve training strategies. The observed differences between experience levels highlight the importance of optimizing the interaction between base and top gymnasts, particularly regarding movement timing and force application. The proposed methodology and the evidence obtained in the present work could improve pairs’ coordination to obtain better throws, both in ACRO and in other sports with similar skills such as cheerleading, figure skating, or artistic swimming.

5. Conclusions

As far as we know, this is the first study to kinematically analyze both individual actions and the interdependence between two subjects during a dynamic skill. We concluded that each role contributes differently to the performance of the skill. The top gymnasts show limited independent movement and are primarily influenced by the base’s motion.

The pair’s experience, along with interpersonal coordination and the skill to anticipate their partner’s motion are key components in ACRO. From a practical standpoint and according to the results found in the ME pairs, to achieve effective throws, pairs should take less time to perform the same task and move faster in the downward motion (s and % time). For the upward motion, higher relative time should be used (more time to push and apply force vertically). For spatial variables, results suggest a shorter range of motion (lower MD Pos and TO Pos), and faster movements (MD Vel and MU Vel). For the individual motion of the top, the strategy used is a lower MD Pos and higher TO Pos.

Coaches and researchers should be aware that ME tops move slower while the bases are pushing them upward, providing greater stability and facilitating force application, which allows ME bases and systems to push faster. Also, both LE and ME tops perform the take-off with enough velocity to achieve the required aerial trajectory, and not necessarily with their maximum velocity.

Regarding the anticipatory ability, we suggest shorter time delays in position (~1%) and longer time delays in velocity (~5%) to improve interpersonal coordination. The bases should wait for the top gymnast’s body to stretch fully before pushing upward. Generally, the top GCS is moving ahead of the base. However, when the base gymnast’s contribution is isolated (top LCS), the top gymnast is delayed in relation to the base. Coaches are encouraged to implement tasks that challenge gymnasts’ anticipatory abilities and interpersonal timing to replicate competition demands and consequently enhance motor synergy and performance outcomes.